Remove the giblets from the chicken. Discard the liver (it makes the broth bitter ) and hold onto everything else. Rinse the chicken with cool water. Put the chicken, onion, and giblets in a large stockpot. Pour in enough cold water just to cover by 1 inch (about 3 quarts). Toss in the garlic and herbs and allow the water to slowly come to a boil over medium heat. Skim off the foam then reduce the heat and simmer gently for 1 hour, uncovered, until the chicken is cooked through. Skim any impurities that rise to the surface; add more water if necessary to keep the chicken covered.

Carefully remove the chicken to a cutting board and let it cool. With a slotted spoon, remove the vegetables, giblets, thyme and bay leaf from the pot and discard. Reserve chicken broth . When the chicken is cool enough to handle, discard the skin and bones; shred the meat by hand.

Meanwhile, seed, core, and thinly slice the poblano peppers.

Heat a 2-count of olive oil in a medium saucepan over medium heat. Add the onion and garlic and cook until softened, about 5 minutes. Dust the vegetables with the ground cumin, coriander , and oregano , and stir; cook 1 minute. Stir in the ground tortillas. Pour in the reserved chicken broth, season with salt and cook 20 minutes. Now add the shredded chicken and chiles, and the cilantro and cook 5 more minutes. Taste for seasoning.

To serve, ladle the chili into big bowls and garnish with grated cheese, cilantro, and a wedge of lime. Serve with the Smoky Chile Cornbread